The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory m...
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| Formato: | Objeto de conferencia |
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2011
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/167657 |
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I19-R120-10915-1676572024-07-01T20:01:59Z http://sedici.unlp.edu.ar/handle/10915/167657 The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance Michtchenko, Tatiana Alexandrovna Ferraz-Mello, Sylvio Beaugé, Cristian 2011-07 2012 2024-07-01T17:34:54Z en Ciencias Astronómicas mean-motion resonance chaotic motions apsidal corotation resonances We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory motion of the angle between the pericentres (Aw-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as internal and external resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is 2 λ₂ — λ₁— ͞ω₁, where λᵢ and Wi stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is 2 λ₂ — λ₁ — ͞ω₂. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to- moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria. Facultad de Ciencias Astronómicas y Geofísicas Objeto de conferencia Objeto de conferencia http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf 247-262 |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Ciencias Astronómicas mean-motion resonance chaotic motions apsidal corotation resonances |
| spellingShingle |
Ciencias Astronómicas mean-motion resonance chaotic motions apsidal corotation resonances Michtchenko, Tatiana Alexandrovna Ferraz-Mello, Sylvio Beaugé, Cristian The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| topic_facet |
Ciencias Astronómicas mean-motion resonance chaotic motions apsidal corotation resonances |
| description |
We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory motion of the angle between the pericentres (Aw-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system.
Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as internal and external resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is 2 λ₂ — λ₁— ͞ω₁, where λᵢ and Wi stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is 2 λ₂ — λ₁ — ͞ω₂. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to- moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria. |
| format |
Objeto de conferencia Objeto de conferencia |
| author |
Michtchenko, Tatiana Alexandrovna Ferraz-Mello, Sylvio Beaugé, Cristian |
| author_facet |
Michtchenko, Tatiana Alexandrovna Ferraz-Mello, Sylvio Beaugé, Cristian |
| author_sort |
Michtchenko, Tatiana Alexandrovna |
| title |
The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| title_short |
The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| title_full |
The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| title_fullStr |
The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| title_full_unstemmed |
The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| title_sort |
periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance |
| publishDate |
2011 |
| url |
http://sedici.unlp.edu.ar/handle/10915/167657 |
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| _version_ |
1807223541477670912 |